An association (dependence) exists between two variables if a particular value/category for one variable is more likely to occur with certain values/categories of the other variable.
Useful for looking at the associations between two categorical variables.
The original table was:
Let's have an example and assume that:
Looking at this table:
We can see that men are more likely to say YES.
If there is no association between OS and Gen, then the conditional proportions for the response variable categories (OS) would be the same for each gender, like this:
In this case the two variables are said to be indipendent.
In these examples, for each category of the response we find under which category of the explanatory variable its percentage is greater than the corresponding marginal.
The variables are:
High values of x tend to occur with high values of y
Low values of x tend to occur with low values of y
high values of one variable tend to pair with low values of the other variable
High values of x tend to occur with low values of y
Low values of x tend to occur with high values of y
The strength of the association can be measured through the correlation coefficient.